4 papers
Intermingled basins: Kan's example on the Riemann sphere
Abbas Fakhari, Ale Jan Homburg, Sebastian van Strien
Kan's discovery of dynamical systems with two attractors whose basins of attraction both have full support, featured specific examples of skew product systems of interval diffeomor…
Generalized Horseshoe Maps part I: limit laws and absolute continuity of physical measure
Abbas Fakhari, Mohammad Soufi, Maisam Hedyeloo +1
We apply thermodynamic formalism to a generalized horseshoe map. We prove that a tailored anisotropic Banach space with weighted norms yields a spectral gap for the transfer operat…
Stable local dynamics: expansion, quasi-conformality and ergodicity
Abbas Fakhari, Meysam Nassiri, Hesam Rajabzadeh
In this paper, we study stable ergodicity of the action of groups of diffeomorphisms on smooth manifolds. Such actions are known to exist only on one-dimensional manifolds. The aim…
Thick attractors with intermingled basins
Abbas Fakhari, Ale Jan Homburg
We construct various novel and elementary examples of dynamics with metric attractors that have intermingled basins. A main ingredient is the introduction of random walks along orb…